Properties

Label 123200.gn
Number of curves $2$
Conductor $123200$
CM no
Rank $0$
Graph

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Show commands: SageMath
E = EllipticCurve("gn1")
 
E.isogeny_class()
 

Elliptic curves in class 123200.gn

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
123200.gn1 123200v2 \([0, -1, 0, -2279233, 929702337]\) \(1278763167594532/375974556419\) \(384997945773056000000\) \([2]\) \(3932160\) \(2.6558\)  
123200.gn2 123200v1 \([0, -1, 0, 382767, 96496337]\) \(24226243449392/29774625727\) \(-7622304186112000000\) \([2]\) \(1966080\) \(2.3092\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 123200.gn have rank \(0\).

Complex multiplication

The elliptic curves in class 123200.gn do not have complex multiplication.

Modular form 123200.2.a.gn

sage: E.q_eigenform(10)
 
\(q + 2 q^{3} - q^{7} + q^{9} + q^{11} - 4 q^{17} - 4 q^{19} + O(q^{20})\) Copy content Toggle raw display

Isogeny matrix

sage: E.isogeny_class().matrix()
 

The \(i,j\) entry is the smallest degree of a cyclic isogeny between the \(i\)-th and \(j\)-th curve in the isogeny class, in the LMFDB numbering.

\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)

Isogeny graph

sage: E.isogeny_graph().plot(edge_labels=True)
 

The vertices are labelled with LMFDB labels.